1. Field of the Invention
The present invention relates to apparatus and methods for reducing the spatial resolution of an optical image prior to detection to reduce image aliasing.
2. Description of the Prior Art
In conventional cameras, the lens forms an image of the object on film, where the image is recorded. In digital cameras, the film is replaced by an electronic detector such as a charge coupled device (CCD) or CMOS. An ideal lens that has a small F-number (focal length divided by lens diameter) captures more light and produces an image with higher spatial resolution than does an ideal lens with a large F-number. The amount of light that is captured increases as the square of the aperture diameter, and the theoretical spatial resolution increases linearly with the aperture diameter.
At some point, however, the spatial resolution of the recorded image is limited by the spatial resolution of the digital detector or the spacing of the detector elements. Consequently, increasing the aperture size increases the amount of light gathered, but does not increase the overall spatial resolution of the imaging system. In fact, rather than simply not providing more resolution, the image can become worse as the aperture size increases, once the limit of the image detector is exceeded. This is because the large lens aperture provides excess or wasted spatial resolution that causes aliasing in the recorded image.
Aliasing occurs when the lens presents more spatial detail to the detector array than it can record. The spatial detail that is left over appears as incorrect, less detailed information. That is, the image has errors caused by the detailed information that is masquerading, or aliasing, as less detailed information. The detail limit that the detector array can handle is normally given in terms of line pairs per millimeter of resolution, or in terms of spatial frequency information in cycles per millimeter. When more spatial detail is presented to the detector than it can record, the higher spatial frequency information folds back into the lower frequency region, corrupting the image.
A similar effect occurs in electrical communication signals which are digitized and processed by telephones or television, when higher frequency information is supplied to the system than the system is prepared to process. Generally, the sampling frequency should be at least twice the highest frequency component in the signal. To prevent aliasing, a low pass or anti-aliasing filter is used to remove the high frequency data (analogous to the extra detail in an optical image) before the signal is sampled and processed. Up to now it has not generally been practical to design a low-pass optical spatial frequency filter to remove the excess image detail before the image is detected by the detector array. Many methods have been tried to lower the resolution of the image, with limited success.
The first method is simply to make the lens aperture smaller. This reduces the resolution of the image, but at the cost of reducing the amount of light captured by the system. The exposure time or illumination level must be increased to make up for the reduction of light.
A second method, disclosed in U.S. Pat. No. 2,959,105 and shown in FIGS. 1 and 2, teaches the use of random, coplanar spots or phase steps 2 on an optical element 1, placed near the aperture stop of the imaging system, to provide random phase noise. This type of system is difficult to fabricate, due to specific statistical performance required of the random phase steps and the sharpness required of those steps. A similar system is described in U.S. Pat. No. 4,804,249, and shown in FIG. 3, which teaches the use of a plurality of coplanar optical plateaus on an optical element, the height of any two plateaus differing by more than the coherence length of the illumination, and requires relatively broadband illumination. Such a system is difficult and expensive to fabricate.
A third general method is to replicate the point spread function, resulting in a multiplicity of image points at the storage device for a single object point, thus spreading the light from a single object point over two or more capture elements (such as CCD elements). One example of such a system is disclosed in U.S. Pat. No. 4,989,959, which teaches the use of a pyramidal structure for forming several image points for a given object point. Like any symmetrical element, this element has a misfocus component and can confuse auto-focus systems (i.e. spatial bandwidth of the combined optical/element system is dependent on focus position). FIG. 4 (prior art) illustrates this system. Another system of this type is disclosed in U.S. Pat. No. 5,555,129, which teaches forming a lens having a plurality of regions acting as independent lenses, to form a replicated set of point spread functions. This element attenuates only a narrow range of spatial frequencies and is highly color dependent. FIG. 7 illustrates this element.
FIG. 9 illustrates another system of this type, which was disclosed in an article entitled "Color dependent optical prefilter for the suppression of aliasing artifacts," Applied Optics, vol. 29, no. 5 (Feb. 10, 1990) and described in U.S. Pat. No. 4,575,193. This system utilizes a birefringent crystal (made of quartz or the like) to generate two image points for a given object point (more image points may be generated by crossing a plurality of birefringent crystals). The input light cannot be is polarized, limiting the application of this system. It also takes up considerable space. All of the systems of this type suffer from the same disadvantage, namely that generating several image points for each object point attenuates only a narrow range of spatial frequencies. Expanding these systems to attenuate a greater range of frequencies requires the use of increasingly complex, difficult to fabricate, and bulky elements.
A fourth method involves placing an optical fiber bundle a specific distance from the detector array to deliberately blur the image. The fiber bundle must have the fibers at the output and the input arranged in exactly the same order, must be positioned accurately, and is expensive, difficult to customize, and requires considerable space. An example of this type of system is disclosed in U.S. Pat. No. 5,299,275. FIG. 8 shows the configuration taught in this patent. Element 16 uses the phase modifying characteristics of multimode optical fibers to attenuate high spatial frequency components.
A fifth method involves deliberate use of misfocus or traditional lens aberrations to attenuate certain spatial frequencies. An example of this type of system is disclosed in U.S. Pat. No. 5,438,366, which teaches an element which forms a disk-like image of a single point (shown in FIG. 5). A second example of this type of system is disclosed in U.S. Pat. No. 5,270,825, which teaches utilizing spherical aberration to attenuate high spatial frequencies (shown in FIG. 6). Both of these systems are symmetrical, meaning they include a misfocus component which confuses auto-focus systems.
A need remains in the art for simple and inexpensive apparatus and methods to reduce the spatial resolution of an optical image to prevent aliasing, without requiring a reduction in the amount of light captured by the system, and without adversely affecting image quality or requiring complex optical systems.